Part III, Chapter 13: Of Syllogisms whose Conclusion is Conditional
WE have seen that a proper syllogism cannot have less than three propositions. But this is true only when we obtain a conclusion absolutely, and not when we obtain it conditionally, because then the conditional proposition alone may contain one of the premises, besides the conclusion, and even both.
EXAMPLE.—If I wish to prove that the moon is an uneven body, and not polished like a mirror, as Aristotle believed, I cannot conclude this absolutely, except in three propositions: —
Every body which reflects the light from all its parts is uneven;
Now the moon reflects the light from all its parts; Therefore the moon is an uneven body. But I need only two propositions, in order to conclude conditionally in this way:
Every body which reflects light from all its parts is uneven; Therefore, if the moon reflects the light from all its parts, it is an uneven body.
And I may even include this reasoning in a single proposition, thus: —
If every body which reflects light from all its parts is uneven, and the moon reflects light from all its parts, it must be confessed that it is not a polished body, but uneven.
Or, equally in connecting one of the propositions by the causal particle because, or since—If every true friend ought to be ready to give his life for his friend—there are few true friends, since there are few who are friends to this extent.
This way of reasoning is very common and very good, and hence we are not to imagine there is no reasoning, except when we see three propositions separated and arranged as in the schools, for it is certain that single proposition comprehends this entire syllogism —
Every true friend ought to be ready to give his life for his friend; Now there are few people who are ready to give their lives for their friends; Therefore there are few true friends.
All the difference between these absolute syllogisms, and those in which the conclusion is contained with one of the premises in a conditional proposition, is that the first cannot be conceded entirely, except we agree to that of which it endeavours to persuade us, whereas, in the last, we may concede everything, without the proposer having gained anything thereby, since it remains with him to prove that the condition on which the consequence which was conceded to him rests, is true.
And thus these reasonings are, properly, only preparatory to an absolute conclusion, but they are, nevertheless, very suitable for this purpose; and are, it must also be confessed, very common and natural, while they have this advantage, that being further removed from the manner of the schools, they are, on this account, better received in the world.
We may obtain a conclusion, in this way, in all the figures, and through all the moods; and thus there are no other rules to be observed but the rules of the figures themselves. It is only necessary to remark, that the conditional conclusion always comprehends one of the premises besides the conclusion. This is sometimes the major and sometimes the minor. This will appear from the examples of many conditional propositions, which may be obtained from two general maxims, the one affirmative, and the other negative, whether the affirmation be already proved, or conceded without proof.
Every feeling of pain is a thought. From this we may conclude
1. Therefore, if all brutes feel pain, All brutes think.—Barbara.
2. Therefore, if some plant feels pain,
Some plant thinks.—Darii.
3. Therefore, if all thought is an action of the mind,
All feeling of pain is an action of the mind.—Barbara.
4. Therefore, if all feeling of pain is an evil,
Some thought is an evil.—Darapti.
5. Therefore, if the feeling of pain is in the hand which is burnt, There is some thought in the hand which is burnt—Disamis.
6. Therefore, if there is no thought in the body,
No feeling of pain is in the body.—Celarent.
7. Therefore, if no beast thinks,
No beast feels pain.—Camestres.
8. Therefore, if some part of man does not think,
Some part of man does not feel pain.—Baroco.
9. Therefore, if no movement of matter is a thought,
No feeling of pain is a movement of matter.—Cesare,
10. Therefore, if the feeling of pain is not agreeable,
Some thought is not agreeable.—Felapton.
11. Therefore, if some feeling of pain is not voluntary,
Some thought is not voluntary.—Bocardo.
We may still obtain some other conditional conclusions from this general maxim, Every feeling of pain is a thought; but as these are not very natural, they are not worth enumerating.
Of those which we have given, there are some which comprise the minor in addition to the conclusion,—to wit, 1st, 2d, 7th, 8th; and others, the major,—to wit, the 3d, 4th, 5th, 6th, 9th, 10th, and 11th.
We may, in the same way, notice the different conditional conclusions which may be derived from a general negative proposition, such, for example, as No matter thinks.
1. Therefore, if all the souls of the brutes are matter,
No soul of a brute thinks.—Celarent.
2. Therefore, if some part of man is matter,
Some part of man does not think.—Ferio.
3. Therefore, if our soul thinks,
Our soul is not matter.—Cesare.
4. Therefore, if some part of man thinks,
Some part of man is not matter.—Festino.
5. Therefore, if every thing that feels pain thinks,
No matter feels pain.—Camestres.
6. Therefore, if all matter is a substance,
Some substance does not think.—Felapton.
7. Therefore, if some matter is the cause of many effects which appear very marvellous, Everything which is the cause of marvellous effects does not think.—Ferison.
Of these conditionals there are only five which contain the major in addition to the conclusion; all the others contain the minor.
The greatest use of these kinds of reasoning is to compel him with whom we are discussing to recognise, in the first place, the validity of a consequence which he may allow, without pledging himself to anything further, because it is proposed to him only conditionally, and separated from the true matter, so to speak, which it contains. And hence, he is disposed to receive more easily the absolute conclusion which is derived from it, either by positing the antecedent, in order to posit the consequent, or by taking away the consequent, in order to take away the antecedent.
Thus, a man having granted me that No matter thinks, I may conclude from it, Therefore, if the soul of brutes thinks, it must be distinct from matter. And as he cannot deny me this conditional conclusion, I may obtain from it one or other of these two absolute consequences:—Now the soul of brutes thinks; Therefore it is distinct from matter. Or equally well on the contrary—
Now the soul of brutes is not distinct from matter; Therefore it does not think.
Hence we see that four propositions are necessary, in order to make these kinds of reasonings complete, and to make them establish anything absolutely. We must not, however, place them in the rank of syllogisms which are called compound, because these four propositions contain nothing more in sense than these three propositions of a common syllogism: —
No matter thinks;
Every soul of a brute is matter;
Therefore no soul of a brute thinks.